Related angles

For 90° ± θ and 270° ± θ the function changes to its co-function: sin becomes cos, cos becomes sin, tan becomes cot. The sign is the sign of the original function in the quadrant where the new angle lies (with θ acute). For example sin(90° + θ): the angle is in the second quadrant where sin is positive, so sin(90° + θ) = cos θ. Another: cos(270° − θ): third quadrant, cos negative, so it is −sin θ. In particular sin(90° − θ) = cos θ: the sine of an angle equals the cosine of its complement. To find the ratio of any angle without a calculator: (1) bring it to 0°–360° by adding or subtracting turns; (2) write it as 180° ± θ, 360° − θ and so on with θ a special angle; (3) take the sign from the quadrant; (4) use the special values.